Kieran Richardson, 33, Martin Cranie, 31, and Nigel Reo-Coker, 34, have all travelled to the University of St Andrews in Fife.
Although the main reason behind the move is to help boost the number of experienced players in training sessions, Moore has not ruled out a potential deal if any of them impress him.
“They are three experienced boys that have been in the game,” said Albion’s head coach. “The idea is they’re free agents, their advisors have contacted us, we’ve invited them in to get a free look at them really.
“All three players have grasped the opportunity to train with some elite players.
“It was the perfect fit for me to look at them over the next couple of weeks before making any sort of decision on it.”
Full-back Richardson, who helped Albion pull off the Great Escape in 2005 while on loan from Manchester United, and defender Cranie, who was last on Huddersfield’s books, both featured in the 3-0 win over Barnet last weekend.
Former Villa midfielder Reo-Coker was at MK Dons last season following a spell playing Major League Soccer in the United States.
Moore will not ignore any eye-catching performances in training or pre-season, but he is currently looking elsewhere for recruits.
Albion's head coach is keen to add younger legs to the his squad this summer and confirmed the Baggies have several bids in for players.
“We have offers in for players at the moment,” he said. “Now it’s just trying to agree fees with the clubs we are trying to get them from from and obviously personal terms.
“Hopefully we can get them over the line and see one or two new faces coming to the club.”
Albion are hoping to tie up a deal for around £3.5m for Swansea defender Kyle Bartley in the next week, and are also keen to line up a replacement winger before letting James McClean leave for Stoke.
Goalkeeper Sam Johnstone is the only player to join the club so far this summer following his £6.5m move from United but Moore has been impressed with how he’s trained in Scotland.
“He’s fantastic,” said Moore. “He looks the part, a wonderful character and great person.
“Early signs from what I’ve seen, we’ve got an excellent goalkeeper in Sam. We’re really pleased to have him on board.”